Harmonic Mean

Q.

If H is the harmonic mean between p and q, then the value of $\frac{H}{p}+\frac{H}{q}$ is

1. 2

2. 

3. 

4. 

Q. If H is the harmonic mean between p and q, then the value of $\frac{H}{p}+\frac{H}{q}$ is
[MNR 1990; UPSEAT 2000, 01]

1. $\frac{pq}{p+q}$
2. $\frac{p+q}{pq}$
3. 2
4. None of these

Q. If the harmonic mean between a and b be H, then the value of $\frac{1}{H-a}+\frac{1}{H-b}$ is

1. a+b
2. ab
3. $\frac{1}{a}+\frac{1}{b}$
4. $\frac{1}{a}-\frac{1}{b}$

Q. The harmonic mean of $\frac{a}{1-ab}$ and $\frac{a}{1+ab}$ is
[MP PET 1996; Pb. CET 2001]

1. $\frac{a}{\sqrt{1-a^2{b}^2}}$
2. $\frac{a}{1-a^2{b}^2}$
3. $\frac{1}{1-a^2{b}^2}$
4. a

Q. If $x>1,y>1,z>1$ are in GP, then $\frac{1}{1+lnx},\frac{1}{1+lny},\frac{1}{1+lnz}$ are in

1. AP
2. HP
3. GP
4. None of these

Q. The value of $x+y+zis15ifa,x,y,z,b$ are in A.P. while the value of
$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}is\frac{5}{3}ifa,x,y,z,b$ are in H. P. Then the value of and b are

1. None
2. 2 and 8
3. 1 and 9
4. 3 and 7

Q. If the A.M. between a and b is m times their H.M. then a:b =

1. None of these
2. $\sqrt{m}+\sqrt{m-1}:\sqrt{m}-\sqrt{m-1}$
3. $\sqrt{m}-\sqrt{m-1}:\sqrt{m+1}+\sqrt{m-1}$
4. $\sqrt{m}+\sqrt{m+1}:\sqrt{m}-\sqrt{m+1}$

Q. If $H_1,H_2,\dots \dots ,H_{20}$ be 20 harmonic means between $2$ and $3$, then the value of $\frac{H_1+2}{H_1-2}+\frac{H_{20}+3}{H_{20}-3}$ is

1. $20$
2. $21$
3. $40$
4. $41$

Q. If $b-c,2b-x$ and $b-a$ are in $H.P.$ then $a-\frac{x}{2},b-\frac{x}{2}$ and $c-\frac{x}{2}$are in

1. $A.P.$
2. $G.P.$
3. $H.P.$
4. None

Q. If $a,b,c$ are in $H.P.,$ then $\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in

1. $A.P.$
2. $G.P.$
3. $H.P.$
4. None